Invertibility of Sobolev mappings under minimal hypotheses

Leonid V. Kovalev; Jani Onninen; Kai Rajala

doi:10.1016/j.anihpc.2009.09.010

Invertibility of Sobolev mappings under minimal hypotheses

Leonid V. Kovalev, Jani Onninen, Kai Rajala

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W^{1, n} mapping is a local homeomorphism if it has integrable inner distortion function and satisfies a certain differential inclusion. The integrability assumption is shown to be optimal.

Original language	English (US)
Pages (from-to)	517-528
Number of pages	12
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	27
Issue number	2
DOIs	https://doi.org/10.1016/j.anihpc.2009.09.010
State	Published - 2010

Keywords

Differential inclusion
Finite distortion
Local homeomorphism

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2009.09.010

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title = "Invertibility of Sobolev mappings under minimal hypotheses",

abstract = "We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W1, n mapping is a local homeomorphism if it has integrable inner distortion function and satisfies a certain differential inclusion. The integrability assumption is shown to be optimal.",

keywords = "Differential inclusion, Finite distortion, Local homeomorphism",

author = "Kovalev, {Leonid V.} and Jani Onninen and Kai Rajala",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (L.V. Kovalev), [email protected] (J. Onninen), [email protected] (K. Rajala). 1 Supported by the NSF grant DMS-0913474. 2 Supported by the NSF grant DMS-0701059. 3 Supported by the Academy of Finland.",

year = "2010",

doi = "10.1016/j.anihpc.2009.09.010",

language = "English (US)",

volume = "27",

pages = "517--528",

journal = "Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire",

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publisher = "European Mathematical Society Publishing House",

number = "2",

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TY - JOUR

T1 - Invertibility of Sobolev mappings under minimal hypotheses

AU - Kovalev, Leonid V.

AU - Onninen, Jani

AU - Rajala, Kai

N1 - Funding Information: * Corresponding author. E-mail addresses: [email protected] (L.V. Kovalev), [email protected] (J. Onninen), [email protected] (K. Rajala). 1 Supported by the NSF grant DMS-0913474. 2 Supported by the NSF grant DMS-0701059. 3 Supported by the Academy of Finland.

PY - 2010

Y1 - 2010

N2 - We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W1, n mapping is a local homeomorphism if it has integrable inner distortion function and satisfies a certain differential inclusion. The integrability assumption is shown to be optimal.

AB - We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W1, n mapping is a local homeomorphism if it has integrable inner distortion function and satisfies a certain differential inclusion. The integrability assumption is shown to be optimal.

KW - Differential inclusion

KW - Finite distortion

KW - Local homeomorphism

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U2 - 10.1016/j.anihpc.2009.09.010

DO - 10.1016/j.anihpc.2009.09.010

M3 - Article

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VL - 27

SP - 517

EP - 528

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 2

ER -

Invertibility of Sobolev mappings under minimal hypotheses

Abstract

Keywords

ASJC Scopus subject areas

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